I just finished reading mom's entire FB and it is full of rapidly cycling mood swings - happy, sad, angry, girlish gushing, resentful, happy, sad, up, down, empty, angry - literally from one day to next. Her FB only goes back a couple of years where she initially talks a lot about sobriety and meetings and whatnot, so it appears she was already an addict when she started FBing. I don't know if this unstable mood pattern was a direct result of her drug use or if it's always been a part of her psychology, but she is definitely all over the place and in need of some serious intervention - whether it's substance abuse treatment or treatment for a general mental illness, I do not know, but she is really ill.
Having thought about what I read in her postings, in her own words, I'm on the fence as to whether or not she was capable of deliberately and overtly killing her baby in an act of violence. Apathy, lack of care, starvation, drug overdose or some other passive action like simply dropping the baby into the canal alive I can see her doing. She mentions that she has a felony record but doesn't say what the charge was for, so I don't know if it was a violent charge or not, but nothing in her FB (or the other 5 or 6 I read) referenced any kind of violent behavior or outbursts on her part.
Now, dad is a different story. He has severe and aggressive violent outbursts like battery and assault with a deadly weapon convictions - all against weaker females, not males. I suspect if outright violence or battery lead to the death of this infant, it is much more likely that he committed the act rather than her. I also suspect his drug problem is much, much worse than hers as his appearance now compared to two years ago is alarmingly deteriorated, whereas she looks no better or worse than usual really.
I think an act of explosive violence took place in that house after grandpa left on the 9th, which is why mom refused to answer the door when grandma came by later that day to check on things. And why no one has seen this infant since that day. My money is on dad - with mom sticking by him and covering up the murder of the baby to protect him. If it was the other way around, I think he'd throw her under the bus in a heartbeat.
As always, this is only an opinion.